Abstract
In this paper, we investigate a spatialS–I model with non-linearincidence rates βSpIq, and obtain the conditions for transcritical bifurcation, Hopf bifurcation and Turingbifurcation. In particular, the exact Turing domain is found in the parameter space. Forparameters are in that domain, a series of numerical simulations reveal that the model has richdynamics. In our previous paper (Liu and Jin, 2007 J. Stat. Mech. P05002), we considered anepidemic model with constant rate of removal of the infectives and the mass action incidenceβSI, in which only a stripe pattern was observed. However, in this paper, we obtain not only astripe-like pattern but also a spot pattern, or coexistence of the two. The results obtainedextend well the finding of pattern formation in the epidemic model and may well explainthe field observed in some areas.
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